Several result on SD-prime cordial graphs

Abstract

A bijection f: V(G) → {1,2,··· ,|V(G)|} induces an edge labeling f∗: E(G) → {0,1} such that for any edge uv in G, f∗(uv) = 1 if gcd(S,D) = 1 and f∗(uv) = 0 otherwise, where S = f(u)+ f(v) and D = |f(u)− f(v)|. The labeling f is called SD-prime cordial labeling if |ef∗(0) − ef∗(1)|≤1. We say that G is SD-prime cordial graph if it admits SD-prime cordial labeling. In this paper, we prove that certain classes of zero-divisor graphs of commutative rings are SD-prime cordial graphs.